Have you seen this way of doing multiplication ?

A collection of resources to support work on Factors and Multiples at Secondary level.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

Explore the relationship between simple linear functions and their graphs.

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Given the products of diagonally opposite cells - can you complete this Sudoku?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

Can you find what the last two digits of the number $4^{1999}$ are?

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

Find the highest power of 11 that will divide into 1000! exactly.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Can you find any perfect numbers? Read this article to find out more...

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

A game that tests your understanding of remainders.

Substitution and Transposition all in one! How fiendish can these codes get?

Can you work out what size grid you need to read our secret message?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?